Dzsudzsák made his debut in the Hungarian National Championship as a young lad in 2004. He played twice during his first season in Debreceni VSC. In his second season he played ten matches and scored two goals. In the following two seasons he became a permanent member of the squad, playing 36 matches and scoring 12 goals. He won the Hungarian National Championship three times in 2005, 2006, and 2007. Dzsudzsák won the Hungarian Super Cup three times in 2005, 2006, and 2007.